Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the radius of a circle is doubled, its area is increased by
(a)100\%
(b)200\%
(c)300\%
(d)400\%
Answer
Answer (as printed): C
Explanation
Let the original radius be $R$. New radius $=2 R$. Original area $=\pi R^{2}$, New area $=\pi(2 R)^{2}=4 \pi R^{2}$. Increase in area $=\left(4 \pi R^{2}-\pi R^{2}\right)=3 \pi R^{2}$. $$\text { Increase } \%=\left(\frac{3 \pi R^{2}}{\pi R^{2}} \times 100\right) \%=300 \% \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.